The lawsuit is the first after the Department of Homeland Security’s announcement Monday that it would deny green cards to migrants who use Medicaid, food stamps, housing vouchers or other forms of public assistance.

In their filing, the two counties argued that the rules will worsen the health and well-being of their residents, increase public health risks and financially harm the counties. The rules, they argued, would result in a “chilling effect” in which migrants forgo or disenroll from federal public assistance programs to reduce the risk of green card denial. This would mean that the cost of services would shift from federal to state governments.

The counties also argued that the rules undermine Congress’ broader system of immigration laws that prioritizes family unification and that the federal government did not sufficiently offer rationale to explain the alleged benefits of the rules or justify its costs.

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This rule “makes it easier to unfairly target hard-working, lawful immigrants while sowing fear and confusion in our communities,” San Francisco City Atty. Dennis Herrera said in a statement. “This rule forces people to make an impossible choice: their health or a better future for their family. We will all bear the cost of this misguided policy.”

Federal law currently requires those seeking to become permanent residents or gain legal status to prove they will not be a burden to the U.S. — a “public charge,” in government speak — but the new rules detail a broader range of programs that could disqualify them.

Under the new rules, the Department of Homeland Security has redefined a public charge as someone who is “more likely than not” to receive public benefits for more than 12 months within a 36-month period. U.S. Citizenship and Immigration Services will now weigh whether applicants have received public assistance along with other factors such as education, income and health to determine whether to grant legal status.

Multiple lawsuits were expected. Hours after the rule was published Monday, the Los Angeles-based National Immigration Law Center vowed to sue over what it called an attempt to redefine the legal immigration system to “disenfranchise communities of color and favor the wealthy.” Attorneys general in California and New York said they were also prepared to take legal action.